This invention relates to payout distributions for games of chance.
In a typical game of chance, a player plays the game repeatedly. For each play, he places something of value at risk and receives either no payout or a payout of value. The payout of value can be in any form. Some examples are coins, tokens, credits, or tickets. Each play can result in different levels of payout (for example, payouts at levels of $0, $10, $20, and $100) and each payout level has a probability. For example, each play may have a probability of 5% of producing a payout at the $100 level, a probability of 20% of a $20 payout, 20% for a $10 payout, and 55% for a payout of $0.
The different levels of payout and the probability of each payout level occurring on a given play is called the payout distribution. In some games, such as some card games, the payout distribution is determined by the rules of the game. In other games, such as typical mechanized games of chance (e.g., slot machines), the manufacturer or operator of the game (which we will call the house) can set the payout distribution (in the case of slot machines, the frequencies and payouts are expressed on a so called “par sheet.”).
For example, if a slot machine has 30,000 possible reel positions, there are 30,000 equally possible outcomes for each play. Of these outcomes, a certain number are set to result in a particular payout amount. If 1800 of the possible outcomes are set to produce a payout of 5 coins, a player will win 5 coins in 6% of his plays. If 900 of the possible outcomes are set to produce a payout of 10 coins, a player will win 10 coins in 3% of his plays. The sum of the percentages for all of the possible non-zero payouts is called the hit rate.
The house typically offers multiple units of the game (e.g., rooms full of slot machines) to large numbers of players. The payout distribution to the players determines both the house hold (the average fraction of the payer's at-risk value which the house retains as gross profit) and the quality of the experience for players of the game.
Games having the same hold can produce widely different experiences for players.
For instance, consider two games which both have a hold of 10% and which require the player to risk one dollar to play. Suppose one game produces only a single $1,000,000 payout on average every 1.1 million plays and the other produces a single $10 payout on average every 11.1 plays. From the point of view of the house, these games are essentially the same in that the long-term hold is 10% of money that players put at risk.
However, the players of the two games have much different experiences.
The first game can provide the thrill of a potential million-dollar windfall, but very few people ever experience it. The second game provides a much more modest payout, but the payout is still ten times the price of a single play, and anyone can experience it if he is moderately persistent in playing. If each game is played once every ten seconds 24 hours per day, the first game produces an average of only 2.9 winners per year while the second game produces an average of 864 winners per day.
The gaming industry often characterizes games by their hold, their hit rate (the frequency with which a player wins a payout of any amount), and their volatility (the expected volatility in the percentage of hold as a function of the number of plays).